My cookies unfortunately came out looking more like flat almond meringues than the cookies resembled in the picture. Does anyone have any idea wha...

I really don't think the almonds were your problem. Unless you processed them until they formed a clump, and were nearly nut butter- then the oil they released might be a small challenge. I really think the trouble lies with the extract, and some older egg whites. Most extracts are almost completely alcohol based, except for the tiny amount of bitter almond oil added in for the flavoring. Egg whites are a fairly neutral pH when fresh, but as they age the pH goes up. That interferes with their ability to foam- and therefore a meringue. The usual counter to this is to add in cream of tartar, an acid which brings down the pH again. Short of doing kitchen chemistry experiments, it's hard to date the age of an egg sometimes. So that's why it's easier to just add in the cream of tartar, or use dried egg whites, or a meringue powder. Give it another whirl using one of those things, and I think you will have success. Just grind the nuts to a fine state, but not until it clumps, and it will be okay to use.

Did you use almond flavoring that was oil or alcohol based? If you used one that was primarily oil based, as in almond oil, that could likely be the problem. This recipe depends on the air whipped into the whites to achieve the shape and texture, and oil causes the meringue to collapse. Some say that the age of your eggs can also play a part, with the whites of older eggs not holding up as well as newer egg whites. Sometimes it can also be the way you are whipping the whites as well. You want to start out a bit slow, and only start building up to speed once the whites have gotten foamy. Otherwise you create great big bubbles, instead of a mesh of tiny ones, and they can't hold up in the mixing or baking. When I make meringue for cookies, I prefer to use a stabilizer to help avoid troubles- usually a pinch of cream of tartar. You might also consider using a meringue powder, which usually already contains stabilizers to help. Sometimes it's just easier that way.